# Inductance calculation of high-speed slotless permanent magnet machines

Sultan Jumayev (Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands)
Aleksandar Borisavljevic (Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands)
Konstantin Boynov (Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands)
Juha Pyrhönen (Department of Electrical Engineering, Lappeenranta University of Technology, Lappeenranta, Finland)
Elena A. Lomonova (Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands)

ISSN: 0332-1649

Article publication date: 2 March 2015

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## Abstract

### Purpose

The purpose of this paper is to give a simple, fast and universal inductance calculation approach of slotless-winding machines and comparison of inductances of toroidal, concentrated and helical-winding machines, since these winding types are widely used among low-power PM machines.

### Design/methodology/approach

Harmonic modeling approach is applied to model the magnetic field of the windings in order to calculate the synchronous inductances. The method is based on distinction between electromagnetic properties of different regions in the machine where each region is represented by its own governing equation describing the magnetic field. The governing equations are obtained from Maxwell’s equations by introducing vector potential in order to simplify the calculations.

### Findings

Results of the inductances of toroidal, concentrated and helical-winding slotless PM machines, which have the same torque and dimensions, obtained by the proposed analytical method are in good agreement with 3D FEM, where the relative difference is smaller than 15 percent. However, the calculation time of the analytical method is significantly less than in 3D FEM: seconds vs hours. Additionally, from the results it is concluded that the toroidal-winding machine has the highest inductance and DC resistance values among considered machines. Helical-winding machine has lowest inductance and DC resistance values. Inductance of concentrated-winding machine is between inductance of helical and toroidal windings; however, DC resistance of the concentrated windings is comparable with resistance toroidal windings.

### Originality/value

In this paper the inductance calculation based on harmonic modeling approach is extended for toroidal and helical-winding machines which makes the method applicable for most of the slotless machine types.

## Citation

Jumayev, S., Borisavljevic, A., Boynov, K., Pyrhönen, J. and Lomonova, E.A. (2015), "Inductance calculation of high-speed slotless permanent magnet machines", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 34 No. 2, pp. 413-427. https://doi.org/10.1108/COMPEL-08-2014-0207

## Publisher

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Emerald Group Publishing Limited